In recent years, a strong debate has emerged in the hydrologic literature regarding how to properly treat nontraditional error residual distributions and quantify parameter and predictive uncertainty. Particularly, there is strong disagreement whether such uncertainty framework should have its roots within a proper statistical (Bayesian) context using Markov chain Monte Carlo (MCMC) simulation techniques, or whether such a framework should be based on a quite different philosophy and implement informal likelihood functions and simplistic search methods to summarize parameter and predictive distributions. This paper is a follow-up of our previous work published in Vrugt and Sadegh (2013) and demonstrates that approximate Bayesian computation (ABC) bridges the gap between formal and informal statistical model-data fitting approaches. The ABC methodology has recently emerged in the fields of biology and population genetics and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics that measure the distance of each model simulation to the data. This paper further studies the theoretical and numerical equivalence of formal and informal Bayesian approaches using discharge and forcing data from different watersheds in the United States, in particular generalized likelihood uncertainty estimation (GLUE). We demonstrate that the limits of acceptability approach of GLUE is a special variant of ABC if each discharge observation of the calibration data set is used as a summary diagnostic. © 2013 Author(s).

A significant portion of present-day soil and Earth science research is computational, involving complex data analysis pipelines, advanced mathematical and statistical models, and sophisticated computer codes. Opportunities for scientific progress are greatly diminished if reproducing and building on published research is difficult or impossible due to the complexity of these computational systems. Vadose Zone Journal (VZJ) is launching a Reproducible Research (RR) program in which code and data underlying a research article will be published alongside the article, thereby enabling readers to analyze data in a manner similar to that presented in the article and build on results in future research and applications. In this article, we discuss reproducible research, its background and use across other disciplines, its value to the scientific community, and its implementation in VZJ.

Experimental design and data collection constitute two main steps of the iterative research cycle (aka the scientific method). To help evaluate competing hypotheses, it is critical to ensure that the experimental design is appropriate and maximizes information retrieval from the system of interest. Scientific hypothesis testing is implemented by comparing plausible model structures (conceptual discrimination) and sets of predictions (predictive discrimination). This research presents a new Discrimination-Inference (DI) methodology to identify prospective data sets highly suitable for either conceptual or predictive discrimination. The DI methodology uses preposterior estimation techniques to evaluate the expected change in the conceptual or predictive probabilities, as measured by the Kullback-Leibler divergence. We present two case studies with increasing complexity to illustrate implementation of the DI for maximizing information withdrawal from a system of interest. The case studies show that highly informative data sets for conceptual discrimination are in general those for which between-model (conceptual) uncertainty is large relative to the within-model (parameter) uncertainty, and the redundancy between individual measurements in the set is minimized. The optimal data set differs if predictive, rather than conceptual, discrimination is the experimental design objective. Our results show that DI analyses highlight measurements that can be used to address critical uncertainties related to the prediction of interest. Finally, we find that the optimal data set for predictive discrimination is sensitive to the predictive grouping definition in ways that are not immediately apparent from inspection of the model structure and parameter values. Key Points: We present a metric to quantify conceptual and predictive discrimination The expected discrimination of prospective data points are calculated Optimal data points depend on between-model variance and information redundancy

© 2015. American Geophysical Union. All Rights Reserved. Experimental design and data collection constitute two main steps of the iterative research cycle (aka the scientific method). To help evaluate competing hypotheses, it is critical to ensure that the experimental design is appropriate and maximizes information retrieval from the system of interest. Scientific hypothesis testing is implemented by comparing plausible model structures (conceptual discrimination) and sets of predictions (predictive discrimination). This research presents a new Discrimination-Inference (DI) methodology to identify prospective data sets highly suitable for either conceptual or predictive discrimination. The DI methodology uses preposterior estimation techniques to evaluate the expected change in the conceptual or predictive probabilities, as measured by the Kullback-Leibler divergence. We present two case studies with increasing complexity to illustrate implementation of the DI for maximizing information withdrawal from a system of interest. The case studies show that highly informative data sets for conceptual discrimination are in general those for which between-model (conceptual) uncertainty is large relative to the within-model (parameter) uncertainty, and the redundancy between individual measurements in the set is minimized. The optimal data set differs if predictive, rather than conceptual, discrimination is the experimental design objective. Our results show that DI analyses highlight measurements that can be used to address critical uncertainties related to the prediction of interest. Finally, we find that the optimal data set for predictive discrimination is sensitive to the predictive grouping definition in ways that are not immediately apparent from inspection of the model structure and parameter values.

The flow duration curve is a signature catchment characteristic that depicts graphically the relationship between the exceedance probability of streamflow and its magnitude. This curve is relatively easy to create and interpret, and is used widely for hydrologic analysis, water quality management, and the design of hydroelectric power plants (among others). Several mathematical expressions have been proposed to mimic the FDC. Yet, these efforts have not been particularly successful, in large part because available functions are not flexible enough to portray accurately the functional shape of the FDC for a large range of catchments and contrasting hydrologic behaviors. Here, we extend the work of Vrugt and Sadegh (2013) and introduce several commonly used models of the soil water characteristic as new class of closed-form parametric expressions for the flow duration curve. These soil water retention functions are relatively simple to use, contain between two to three parameters, and mimic closely the empirical FDCs of 430 catchments of the MOPEX data set. We then relate the calibrated parameter values of these models to physical and climatological characteristics of the watershed using multivariate linear regression analysis, and evaluate the regionalization potential of our proposed models against those of the literature. If quality of fit is of main importance then the 3-parameter van Genuchten model is preferred, whereas the 2-parameter lognormal, 3-parameter GEV and generalized Pareto models show greater promise for regionalization.

Although plant photosynthetic capacity as determined by the maximum carboxylation rate (i.e., Vc,max25) and the maximum electron transport rate (i.e., Jmax25) at a reference temperature (generally 25 °C) is known to vary considerably in space and time in response to environmental conditions, it is typically parameterized in Earth system models (ESMs) with tabulated values associated with plant functional types. In this study, we have developed a mechanistic model of leaf utilization of nitrogen for assimilation (LUNA) to predict photosynthetic capacity at the global scale under different environmental conditions. We adopt an optimality hypothesis to nitrogen allocation among light capture, electron transport, carboxylation and respiration. The LUNA model is able to reasonably capture the measured spatial and temporal patterns of photosynthetic capacity as it explains ∼55% of the global variation in observed values of Vc,max25 and ∼65% of the variation in the observed values of Jmax25. Model simulations with LUNA under current and future climate conditions demonstrate that modeled values of Vc,max25 are most affected in high-latitude regions under future climates. ESMs that relate the values of Vc,max25 or Jmax25 to plant functional types only are likely to substantially overestimate future global photosynthesis.

The development and application of evolutionary algorithms (EAs) and other metaheuristics for the optimisation of water resources systems has been an active research field for over two decades. Research to date has emphasized algorithmic improvements and individual applications in specific areas (e.g. model calibration, water distribution systems, groundwater management, river-basin planning and management, etc.). However, there has been limited synthesis between shared problem traits, common EA challenges, and needed advances across major applications. This paper clarifies the current status and future research directions for better solving key water resources problems using EAs. Advances in understanding fitness landscape properties and their effects on algorithm performance are critical. Future EA-based applications to real-world problems require a fundamental shift of focus towards improving problem formulations, understanding general theoretic frameworks for problem decompositions, major advances in EA computational efficiency, and most importantly aiding real decision-making in complex, uncertain application contexts.